

# using dfs for finding eulerian path traversal


def 					_UpperCAmelCase				(						a__  ,	a__  ,	a__  ,	a__=None):

			'''simple docstring'''



			a_						:						List[Any] 							= (path or []) + [u]
			for v in graph[u]:
						if visited_edge[u][v] is False:
									a_							,					a_						:						Dict 							= True, True
									a_						:						Union[str, Any] 							= dfs(a__  ,	a__  ,	a__  ,	a__)
			return path


def 					_UpperCAmelCase				(						a__  ,	a__):

			'''simple docstring'''



			a_						:						List[str] 							= 0
			a_						:						List[Any] 							= -1
			for i in range(a__):
						if i not in graph.keys():
									continue
						if len(graph[i]) % 2 == 1:
									odd_degree_nodes += 1
									a_						:						Any 							= i
			if odd_degree_nodes == 0:
						return 1, odd_node
			if odd_degree_nodes == 2:
						return 2, odd_node
			return 3, odd_node


def 					_UpperCAmelCase				(						a__  ,	a__):

			'''simple docstring'''



			a_						:						str 							= [[False for _ in range(max_node + 1)] for _ in range(max_node + 1)]
			a_							,					a_						:						List[Any] 							= check_circuit_or_path(a__  ,	a__)
			if check == 3:
						print("""graph is not Eulerian""")
						print("""no path""")
						return
			a_						:						Optional[int] 							= 1
			if check == 2:
						a_						:						Tuple 							= odd_node
						print("""graph has a Euler path""")
			if check == 1:
						print("""graph has a Euler cycle""")
			a_						:						int 							= dfs(a__  ,	a__  ,	a__)
			print(a__)


def 					_UpperCAmelCase				(						):

			'''simple docstring'''



			a_						:						int 							= {1: [2, 3, 4], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [4]}
			a_						:						List[Any] 							= {1: [2, 3, 4, 5], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [1, 4]}
			a_						:						int 							= {1: [2, 3, 4], 2: [1, 3, 4], 3: [1, 2], 4: [1, 2, 5], 5: [4]}
			a_						:						int 							= {1: [2, 3], 2: [1, 3], 3: [1, 2]}
			a_						:						Any 							= {
			    1: [],
			    2: []
			    # all degree is zero
			}
			a_						:						Optional[Any] 							= 1_0
			check_euler(a__  ,	a__)
			check_euler(a__  ,	a__)
			check_euler(a__  ,	a__)
			check_euler(a__  ,	a__)
			check_euler(a__  ,	a__)


if __name__ == "__main__":
	main()





__snake_case				:      int   		=			[
    """Audio""",
    """Array2D""",
    """Array3D""",
    """Array4D""",
    """Array5D""",
    """ClassLabel""",
    """Features""",
    """Sequence""",
    """Value""",
    """Image""",
    """Translation""",
    """TranslationVariableLanguages""",
]
from .audio import Audio
from .features import ArrayaD, ArrayaD, ArrayaD, ArrayaD, ClassLabel, Features, Sequence, Value
from .image import Image
from .translation import Translation, TranslationVariableLanguages


